Finite Group Databasebeta

← Group #13150745

Character table — Group #13150745

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12223446661212121224661212336666663666666666661212121212121212121212121212121244442244444444121212121212121266121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-111-111-1-11111-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-11111-1-1
χ911111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-111-11-111-1-111-1-11-11-11-11-1
χ1011111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-111-11-1111-1-111-1-1-11-11-11-11
χ1111111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-11-1-11-1-111-1-1111-11-1-11-11
χ1211111-1-1111-1-1-1-11-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-111-1-1-111-1-111-11-111-11-1
χ1311111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-11-11-11-1-111-111-1-1-1-1111-1-111-1-11
χ1411111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1111-1-11-1-1111-1-1-1-111-111-1-111-1
χ1511111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1111-1-11-11-11-11-1-11111-1-11-1-11-111-1
χ1611111-1-1111-1-1-1-1-11-1-111111111111-1-1-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111-11-1-1111-11-1-1-11111-1-1-111-11-1-11
χ17222222222222222222222-12-1-12-12-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000220000220000000000-1-1-1-10000
χ18222222222222222222222-12-1-12-12-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-20000-2-2000000000011110000
χ1922222222222222222222-12-122-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000002200022000000000000-1-1-1-1
χ2022222222222222222222-12-122-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000-2-2000-2-20000000000001111
χ2122222222222222-2-2-2-2-2-22-12-1-12-12-1-2-211-1-11111-1-1-11122-2-2-1-1-1-111110000220000-2-20000000000-1-1110000
χ2222222222222222-2-2-2-2-2-22-12-1-12-12-1-2-211-1-11111-1-1-11122-2-2-1-1-1-111110000-2-2000022000000000011-1-10000
χ2322222222222222-2-2-2-2-2-2-12-122-12-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-11111000000022000-2-200000000000011-1-1
χ2422222222222222-2-2-2-2-2-2-12-122-12-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-111110000000-2-200022000000000000-1-111
χ2522222-2-2222-2-2-2-22-222-2-22-12-1-12-12-122-1-1-1-1-1-1-1-1-11111-2-2-2-21111111100002-200002-20000000000-11-110000
χ2622222-2-2222-2-2-2-22-222-2-22-12-1-12-12-122-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-220000-2200000000001-11-10000
χ2722222-2-2222-2-2-2-22-222-2-2-12-122-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111111100000002-20002-2000000000000-11-11
χ2822222-2-2222-2-2-2-22-222-2-2-12-122-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2-21111111111110000000-22000-220000000000001-11-1
χ2922222-2-2222-2-2-2-2-22-2-2222-12-1-12-12-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-100002-20000-220000000000-111-10000
χ3022222-2-2222-2-2-2-2-22-2-2222-12-1-12-12-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-10000-2200002-200000000001-1-110000
χ3122222-2-2222-2-2-2-2-22-2-222-12-122-12-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-100000002-2000-220000000000001-1-11
χ3222222-2-2222-2-2-2-2-22-2-222-12-122-12-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-10000000-220002-2000000000000-111-1
χ332-22-222-22-2-222-2-200000022-2-22-2-2220000-2-2000022-2002-20022-2-200002i−2i2i−2i00000000002i−2i2i−2i000000000000
χ342-22-222-22-2-222-2-200000022-2-22-2-2220000-2-2000022-2002-20022-2-20000−2i2i−2i2i0000000000−2i2i−2i2i000000000000
χ352-22-22-222-2-2-2-22200000022-2-22-2-2220000-2-200002-2200-2200-2-22200002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ362-22-22-222-2-2-2-22200000022-2-22-2-2220000-2-200002-2200-2200-2-2220000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ3744444444444444444444-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ3844444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000
χ3944444-4-4444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-21-2-2-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4044444-4-4444-4-4-4-4-44-4-444-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4144-4-4400-44-400000000004444-4-4-4-4400004-40000-40000000000000000000000000000000000000000000000
χ4244-4-4400-44-400000000004-24-22-42-4-20000-22000020023−23000000002323−23−23000000000000000000000000000000
χ4344-4-4400-44-400000000004-24-22-42-4-20000-220000200−232300000000−23−232323000000000000000000000000000000
χ4444-4-4400-44-40000000000-24-24-42-42-2−2i32i300-22−2i3−2i32i32i320000000000000000000000000000000000000000000000
χ4544-4-4400-44-40000000000-24-24-42-42-22i3−2i300-222i32i3−2i3−2i320000000000000000000000000000000000000000000000
χ4644-4-4400-44-40000000000-2-2-2-222221−2i32i3001-1i3i3−i3−i3-10023−2300003i−3i3i−3i−3−333000000000000000000000000000000
χ4744-4-4400-44-40000000000-2-2-2-222221−2i32i3001-1i3i3−i3−i3-100−23230000−3i3i−3i3i33−3−3000000000000000000000000000000
χ4844-4-4400-44-40000000000-2-2-2-2222212i3−2i3001-1−i3−i3i3i3-10023−230000−3i3i−3i3i−3−333000000000000000000000000000000
χ4944-4-4400-44-40000000000-2-2-2-2222212i3−2i3001-1−i3−i3i3i3-100−232300003i−3i3i−3i33−3−3000000000000000000000000000000
χ504-44-444-44-4-444-4-40000004-2-42-2-424-20000220000-2-22004-400-2-2220000000000000000000000000000000000
χ514-44-444-44-4-444-4-4000000-242-442-4-2-20000220000-24-400-2200-2-2220000000000000000000000000000000000
χ524-44-444-44-4-444-4-4000000-2-222-222-210000-1-13-33-31-2200-220011-1-13-33-3000000000000000000000000000000
χ534-44-444-44-4-444-4-4000000-2-222-222-210000-1-1-33-331-2200-220011-1-1-33-33000000000000000000000000000000
χ544-44-44-444-4-4-4-4440000004-2-42-2-424-20000220000-22-200-440022-2-20000000000000000000000000000000000
χ554-44-44-444-4-4-4-444000000-242-442-4-2-20000220000-2-44002-20022-2-20000000000000000000000000000000000
χ564-44-44-444-4-4-4-444000000-2-222-222-210000-1-13-33-312-2002-200-1-111-33-33000000000000000000000000000000
χ574-44-44-444-4-4-4-444000000-2-222-222-210000-1-1-33-3312-2002-200-1-1113-33-3000000000000000000000000000000
χ584-4-44400-4-44000000000044-4-4-444-440000-440000-40000000000000000000000000000000000000000000000
χ594-4-44400-4-4400000000004-2-4224-2-4-200−2i32i32-2−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ604-4-44400-4-4400000000004-2-4224-2-4-2002i3−2i32-22i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ614-4-44400-4-440000000000-242-4-4-242-200002-20000200000023−23000023−23−2323000000000000000000000000000000
χ624-4-44400-4-440000000000-242-4-4-242-200002-200002000000−23230000−232323−23000000000000000000000000000000
χ634-4-44400-4-440000000000-2-2222-2-22100−2i32i3-11i3−i3−i3i3-100000023−233i−3i−3i3i−333−3000000000000000000000000000000
χ644-4-44400-4-440000000000-2-2222-2-22100−2i32i3-11i3−i3−i3i3-1000000−2323−3i3i3i−3i3−3−33000000000000000000000000000000
χ654-4-44400-4-440000000000-2-2222-2-221002i3−2i3-11−i3i3i3−i3-100000023−23−3i3i3i−3i−333−3000000000000000000000000000000
χ664-4-44400-4-440000000000-2-2222-2-221002i3−2i3-11−i3i3i3−i3-1000000−23233i−3i−3i3i3−3−33000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022220020020000-1-1-1-1-1-1-1-100000000
χ686666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-200-200-200001111111100000000
χ696666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000222200-200-20000-1-1-1-1111100000000
χ706666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-200200200001111-1-1-1-100000000
χ716666-3-6-6-3-3-333336-6-3-33300000000000000000000000000000000000022-2-200-20020000-1-111-1-11100000000
χ726666-3-6-6-3-3-333336-6-3-333000000000000000000000000000000000000-2-22200200-2000011-1-111-1-100000000
χ736666-3-6-6-3-3-33333-6633-3-300000000000000000000000000000000000022-2-200200-20000-1-11111-1-100000000
χ746666-3-6-6-3-3-33333-6633-3-3000000000000000000000000000000000000-2-22200-2002000011-1-1-1-11100000000
χ756-66-6-36-6-333-3-33300−3i33i3−3i33i30000000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii3−33−300000000
χ766-66-6-36-6-333-3-33300−3i33i3−3i33i3000000000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i−33−3300000000
χ776-66-6-36-6-333-3-333003i3−3i33i3−3i30000000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii−33−3300000000
χ786-66-6-36-6-333-3-333003i3−3i33i3−3i3000000000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i3−33−300000000
χ796-66-6-3-66-33333-3-300−3i33i33i3−3i30000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i3−3−3300000000
χ806-66-6-3-66-33333-3-300−3i33i33i3−3i3000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii−333−300000000
χ816-66-6-3-66-33333-3-3003i3−3i3−3i33i30000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i−333−300000000
χ826-66-6-3-66-33333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii3−3−3300000000
χ831212-12-12-6006-6663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ841212-12-12-6006-66−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-663−63−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-6−636363−63000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).